Exhibit 99.1

Contact: Cathy Kruse

Telephone: 701-572-2020 ext 1

cathy@georesourcesinc.com

FOR IMMEDIATE RELEASE

GeoResources, Inc. Provides an Operations Update

Announces New Eagle Ford Project and Commencement of Operated Bakken Drilling

Houston, Texas, October 4, 2010 - GeoResources, Inc., (NASDAQ: “GEOI”), today provided an operations update.

EAGLE FORD

We have assembled approximately 22,000 net acres in the Eagle Ford trend of Texas and entered into agreements with Ramshorn Investments, Inc. (“Ramshorn”), an affiliate of Nabors Industries LTD (“Nabors”), to jointly acquire additional acreage and implement a drilling and development program. A wholly-owned subsidiary of GeoResources, Inc. retains a 50% working interest (currently about 11,000 net acres) and will serve as operator within an Area of Mutual Interest (“AMI”), located in Southwest Fayette County, Texas, which covers approximately 140,000 acres. Pursuant to the Participation and Joint Operating Agreements, Ramshorn has purchased a 50% interest in the acreage and will drill six horizontal obligation wells for the joint account. In addition, the parties have agreed to acquire additional acreage within the AMI. We intend to begin drilling as soon as reasonably possible, perhaps by the end of 2010.

BAKKEN SHALE OPERATED

On September 25, 2010, we initiated drilling on our Williams County acreage with the Carlson 1-11H well, a Middle Bakken test in Section 11, T157N-R103W. The initial location is a 640 acre drilling unit and we have a 47.5% working interest. We also plan to drill two 1,280 acre spacing units immediately following the Carlson well. Our working interests in these locations are 34% and 35%, respectively.

We have acquired approximately 50,000 net leasehold acres in an AMI covering about 115,000 acres and as mentioned in prior releases, brought in industry partners to participate in development. As operator, we retained a 47.5% working interest, representing approximately 24,000 net acres.

Assuming full development on a 1,280 acre spacing unit basis, we have a majority interest and control about forty (40) units and have working interests in another forty-two (42) units. Where we have a minority interest in a spacing unit, we will continue to focus on increasing our interests; thereby increasing the likelihood that we will be the designated unit operator.

BAKKEN SHALE NON-OPERATED

To date, in our non-operated program located in Mountrail and adjacent counties, we have participated in 72 wells drilled by our primary operator, Slawson Exploration, with a 100% success rate. In addition, we own minor working interests in numerous wells within the Bakken/Three Forks play. Slawson is currently running three drilling rigs and we continue to acquire additional acreage and well interests, when reasonably available.

The following table updates our prior operations releases regarding this project. Generally, we report only the wells operated by Slawson, but may include others where the wells or our interests are meaningful. We do not report our numerous minor interest wells. The table below lists all such 2010 wells as we have included 30 and 60 average production rates, where data is available. We are reporting oil production only, therefore excluding natural gas and equivalents. We expect to participate in approximately 100 wells over the next two years.

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At present, 9 -12 wells are scheduled for the 4th Quarter of 2010 where we expect to have working interests in the 5% to 15% range. Additional wells are in the process of being permitted and scheduled. Completed well costs, including surface equipment and production facilities for single lateral wells drilled on 640 acre units are currently estimated at approximately $5.0 million and at $6.2 million for 1,280 acre units. Recent wells drilled on 640 acre units have had 18-22 frac stages per well, while wells drilled on 1,280 acre units have had up to 41 stage fracs.

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MONTANA

Our first Bakken well in Montana, the Renegade #1-10H has been drilled and is waiting on a frac. The well was drilled in the Middle Bakken on a 640 acre unit. The well is located on our 2,920 gross acre Rip-Rap prospect in Roosevelt County, Montana in Section 10, T26N-R59E. We have a 25% working interest in the well and prospect.

ST. MARTINVILLE

St. Martinville is a shallow oil development project with deeper gas objectives located in St. Martin Parish, Louisiana. We are currently moving onto our first drilling location. We plan to drill four wells during the 4^th Quarter of 2010 and 1^st Quarter of 2011. The first well, the Conoco Fee A-53, is expected to test Miocene-aged, stacked oil objectives ranging from 2,700 to 4,500 feet. Our working interest is 97%. Pending approval of proposed units and drilling permits, we plan to drill three additional wells one of which will be a re-entry of a previously drilled well. Our working interests are expected to be similar to the Conoco Fee. We continue to work the 3-D seismic and subsurface geologic well control and expect to have additional locations. In the event of success in the first four locations, the project could be expanded to include six to ten additional wells. All of these proposed drilling locations have multiple stacked objectives and are above 5,000 feet. We also have drilling objectives for gas and liquids in the Discorbis section at about 10,000 feet. Drilling and completion services and supplies are readily available for this project.

ACQUISITION

In July 2010, GeoResources, acquired several oil and gas properties for a total purchase price of $16.6 million. The acquisition was financed with cash and bank borrowings under our existing credit facility. The acquisition includes 36 operated and 3 non-operated producing wells in close proximity to our Giddings Field. Our working interests vary from 20% to 100% and our net share of production is about 240 barrels of oil equivalent per day (Boepd) with about 67% oil. Productive formations include the Austin Chalk, Buda, Woodbine and other formations. Proved reserves total approximately 900,000 BOE (83% proved developed producing). The acquisition includes approximately 9,700 net acres, which are held by production and prospective in currently productive and deeper formations. With an allocation of $1.0 million to undeveloped acreage, the net price per proved BOE is under $17.50. We believe we can reduce LOE, increase net cash flows, extend field life and thus, increase proved reserves as a result of our operating capability and proximity to existing properties. We also believe we can generate economic drilling opportunities on this acreage.

Comments:

Frank A. Lodzinski, President and CEO of GeoResources, Inc. commented, “We continue to demonstrate that we have the capability and track record to operate profitably and expand our acreage and drilling portfolio. We have developed a substantial presence in the Bakken and Eagle Ford, which, in my view, are the two most attractive resource plays in the industry. Given low gas prices, earlier this year we chose to release our Austin Chalk drilling rig to focus on drilling for oil and liquids. We are not in jeopardy of losing leases in the near term. We made that decision with the knowledge that we would begin our operated drilling in the Bakken and at St. Martinville and were establishing a new acreage

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position for Eagle Ford development. We expect to begin drilling our Eagle Ford acreage late this year or early next year. We are pleased to partner with Ramshorn with the intent of acquiring additional leases and initiating a significant development program. Ramshorn has been an excellent participant in our operated Austin Chalk development program.

Mr. Lodzinski further commented, “In addition, we are excited with the reported results of other operators in Williams County, ND and have initiated drilling on our operated Bakken acreage. We are moving onto our first location at St. Martinville and based on prior drilling results and our extensive work integrating sub-surface and recent 3-D data, we expect that project to result in attractive economic success and lead to additional drilling. Finally, our recent acquisition provides attractive “bolt-on” economics for just the proved developed producing properties in a core area. We believe upside opportunity exists from operations, development and exploration potential. Finally, we have ample cash flow and liquidity to develop our properties and continue to generate additional projects.”

About GeoResources, Inc.

GeoResources, Inc. is an independent oil and gas company engaged in the acquisition and development of oil and gas reserves through an active and diversified program which includes purchases of reserves, re-engineering, and development and exploration activities, currently focused in the Southwest, Gulf Coast and the Williston Basin. For more information, visit our website at www.georesourcesinc.com.

Forward-Looking Statements

Information herein contains forward-looking statements within the meaning of the Private Securities Litigation Reform Act of 1995, which can be identified by words such as “may,” “will,” “expect,” “anticipate,” “estimate” or “continue,” or comparable words. All statements other than statements of historical facts that address activities that the Company expects or anticipates will or may occur in the future are forward-looking statements. Readers are encouraged to read our Form 10-K and Form 10-K/A for the year ended December 31, 2009 and the other SEC reports of the Company and any and all other documents filed with the SEC regarding information about GeoResources for meaningful cautionary language in respect of the forward-looking statements herein. Interested persons are able to obtain free copies of filings containing information about GeoResources, without charge, at the SEC’s Internet site.

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